---
title: "A general framework for unbiased mixed variables distance"
subtitle: "supplementary material"
format:
html:
theme: minty
toc: true
toc-location: left
toc-expand: 2
page-layout: full
code-fold: true
code-tools: true
embed-resources: true
callout-icon: false
bibliography: unbiased_dist_refs.bib
csl: asa.csl
execute:
collapse: true
message: false
warning: false
---
```{r setup}
#| include: false
packages <- c(
"aricode", "cluster", "fpc", "manydist", "patchwork", "tidyverse",
"tidymodels", "varhandle", "vegan", "kdml", "ggplot2", "viridis",
"dplyr", "entropy", "kernlab", "mclust", "Matrix", "philentropy",
"conflicted", "ggnewscale", "glue"
)
invisible(lapply(packages, require, character.only = TRUE))
tidymodels_prefer()
conflict_prefer("select", "dplyr")
conflict_prefer("filter", "dplyr")
conflict_prefer("distance", "philentropy")
# prefer base set operations (if needed later)
conflict_prefer("intersect", "base")
conflict_prefer("setdiff", "base")
canon_method <- function(m) dplyr::recode(m, dkss = "dkps")
# helper: rinomina colonne solo se esistono (non rompe nulla se non ci sono)
canon_cols <- function(df) {
df |> dplyr::rename_with(canon_method, .cols = dplyr::any_of("dkss"))
}
```
Here we provide the code to reproduce the results of the supplementary material of the paper "Unbiased mixed variables distances".
### Data generation
These are the simulation parameers
```{r,eval=TRUE}
reps<-100 # 100 can take 30min
n<-500
k<-2 # Dimension solution
sigma<-0.03 # Noise
porig<-6 # Number of variables corresponding to true config
pnnoise<-0 # Number of numerical noise vars
pcnoise<-0 # Number of categorical noise vars
pn<-2 # Number of numerical variables underying config
pnum<-pn+pnnoise+pcnoise # Total number of numerical vars+noise vars (Needed to know which vars to discretize)
p<-porig+pnnoise+pcnoise # Total number of variables
qoptions<-c(2,3,5,9) # Distribution of the categorical variables corresponding to true config
pcat<-length(qoptions) # Number of cat variables underlying config
methods = c("baseline","naive","hl","hl_add","gower","gudmm","dkss","mod_gower","u_ind","u_dep","u_mix")
method_levels <- c("baseline", "naive", "hl", "hl_add", "gower","gudmm", "dkps", "mod_gower", "u_ind", "u_dep", "u_mix")
my_colors <- c(
# Set B
"baseline" = "#8C564B", # brown
"naive" = "#E377C2", # pink
"hl" = "#9C9E00", # darker yellow-green (better contrast)
"gudmm" = "#FF7F0E", # orange
"dkps" = "#7F7F7F", # darker grey (more visible)
# Set A
"hl_add" = "#9EC5E5", # light blue
"u_ind" = "#2CA02C", # green
"u_dep" = "#D62728", # red
"u_mix" = "#1E90FF",
"gower" = "#FFBF00", # gold
"mod_gower" = "#9467BD" # purple
)
my_shapes <- c(
"baseline" = 16, # filled circle
"naive" = 17, # filled triangle
"hl" = 15, # filled square
"hl_add" = 3, # plus
"gower" = 4, # cross
"gudmm" = 18, # filled diamond
"dkps" = 8, # star
"mod_gower" = 0, # empty square
"u_ind" = 1, # empty circle
"u_dep" = 2, # empty triangle
"u_mix" = 5 # empty diamond
)
```
The considered methods are
#### additive distances
- `baseline`: Manhattan distance on all the standardized numerical variables (before discretization)
- `gower`: classic Gower distance
- `mod_gower`: modified version of the Gower distance, as proposed in @LYNCLP:2024
- `hl_add`: Manhattan distance with scaling of indicators as proposed by
@HennigLiao2013
- `u_ind`: commensurable with simple matching
- `u_dep`: commensurable PCA-scaled numerical and total-variance categorical
- `u_mix`: commensurable Manhattan numerical and total-variance categorical
#### non-additive distances
- `naive`: Euclidean distance on all variables, with one-hot encoded categorical variables.
- `hl`: Euclidean distance with scaling of indicators as proposed by
@HennigLiao2013
- `gudmm`: Generalized Unified Distance Metric for Mixed-type data as proposed by @MS:2023
- `dkps`: Distance using kernel product similarity as proposed by @GT:2024
<!-- The `distance_by_method.r` recalls `manydist` where applicable, and the external functions when needed. -->
### Compute distances: leave one variable out
```{r, eval=FALSE}
library(progress)
pb <- progress_bar$new(
format = " Simulating [:bar] :percent eta: :eta",
total = reps * length(methods),
clear = FALSE,
width = 60
)
# methods = c("baseline","naive","gower","hl","u_dep","u_ind","gudmm","dkss","mod_gower")
generated_datasets = tibble(replicate=1:reps) |>
mutate(dataset = map(.x=replicate, ~generate_dataset(n = n, pn=pn, porig=porig, pnnoise =pnnoise , pcnoise = pcnoise, sigma = sigma, qoptions = qoptions, seed = 1234+.x)),
method=map(.x=replicate,~methods)
) |> unnest(method)|>
left_join(mdist_method_lookup, by = "method")
```
```{r, eval=FALSE}
## a little helper for mdist
run_mdist_within <- function(df, mdist_type, mdist_preset, param_set, outcome = "response") {
x <- df
if (is.character(outcome) && length(outcome) == 1 && outcome %in% names(df)) {
x <- dplyr::select(df, -dplyr::all_of(outcome))
}
if (mdist_type == "preset") {
out <- manydist::mdist(x = x, preset = mdist_preset)
} else if (mdist_type == "custom") {
if (is.null(param_set)) stop("param_set is NULL for mdist_type = 'custom'")
args <- param_set
args$x <- x
out <- do.call(manydist::mdist, args = args)
} else {
stop("Unknown mdist_type: ", mdist_type)
}
if (identical(mdist_type, "preset") && identical(mdist_preset, "gower")) {
out$distance*ncol(x)
}else{
out$distance
}
}
# little helper for the leave one variable out version of mdist
run_lovo <- function(df, mdist_type, mdist_preset, param_set,
outcome = NULL, dims = 2, keep_dist = FALSE,
legacy_gower_sum = FALSE) {
# drop outcome if present
x <- df
if (is.character(outcome) && length(outcome) == 1 && outcome %in% names(df)) {
x <- dplyr::select(df, -dplyr::all_of(outcome))
}
# ---- special case: legacy Gower SUM scaling for LOVO ----
if (legacy_gower_sum && identical(mdist_type, "preset") && identical(mdist_preset, "gower")) {
vars <- names(x)
p_full <- length(vars)
# full
D_full <- manydist::mdist(x = x, preset = "gower")$distance |> as.matrix()
D_full <- D_full * p_full
base_mds <- cmdscale(D_full, eig = TRUE, k = dims)$points[, 1:dims, drop = FALSE]
loo_list <- vector("list", length(vars)); names(loo_list) <- vars
for (i in seq_along(vars)) {
var <- vars[i]
x_sub <- dplyr::select(x, -dplyr::any_of(var))
p_loo <- ncol(x_sub)
D_loo <- manydist::mdist(x = x_sub, preset = "gower")$distance |> as.matrix()
D_loo <- D_loo * p_loo
loo_list[[i]] <- D_loo
}
mad <- vapply(loo_list, function(m) mean(abs(D_full - m)), numeric(1))
cc <- vapply(loo_list, function(m) {
pts <- cmdscale(m, eig = TRUE, k = dims)$points[, 1:dims, drop = FALSE]
congruence_coeff(base_mds, pts)
}, numeric(1))
ac <- sqrt(1 - cc^2)
res <- tibble::tibble(
variable = vars,
mad_importance = mad,
cc_importance = cc,
ac_importance = ac,
mad_normalized = mad / sum(mad)
)
out <- list(results = res, base_mds = base_mds)
if (keep_dist) {
out$full_dist <- D_full
out$loo_dist <- loo_list
}
return(out)
}
# ---- default path: your package's LOVO ----
if (mdist_type == "preset") {
obj <- manydist::lovo_mdist(x = x, preset = mdist_preset, dims = dims, keep_dist = keep_dist)
} else if (mdist_type == "custom") {
if (is.null(param_set)) stop("param_set is NULL for mdist_type = 'custom'")
args <- param_set
args$x <- x
args$dims <- dims
args$keep_dist <- keep_dist
obj <- do.call(manydist::lovo_mdist, args = args)
} else {
stop("Unknown mdist_type: ", mdist_type)
}
obj
}
```
```{r, eval=FALSE}
simulation_structure <- generated_datasets |>
dplyr::mutate(
loo_results = purrr::pmap(
dplyr::pick(dataset, method, mdist_type, mdist_preset, param_set),
\(dataset, method, mdist_type, mdist_preset, param_set) {
pb$tick()
X <- if (method == "baseline") dataset$Xorig else dataset$X
run_lovo(X, mdist_type, mdist_preset, param_set,legacy_gower_sum = (method == "gower"))
}
)
)
save(file="simulation_structure.RData", simulation_structure)
```
```{r, echo=FALSE, eval=TRUE}
load("simulation_structure.RData")
```
```{r}
reference_method = "baseline"
baseline_refs = simulation_structure |>
filter(method == "baseline") |>
select(replicate, baseline_loo = loo_results)
rel_simulation_structure <- simulation_structure |>
dplyr::left_join(baseline_refs, by = "replicate") |>
dplyr::mutate(
loo_results = purrr::map2(.x = loo_results,.y = baseline_loo,
.f = \(res_obj, ref_obj) {
res <- res_obj$results
ref <- ref_obj$results
# join by variable to be safe (order might differ)
dplyr::left_join(
res,
dplyr::select(ref, variable,
ref_mad_normalized = mad_normalized,
ref_ac_importance = ac_importance),
by = "variable"
) |>
dplyr::mutate(
mad_relative_importance = mad_normalized / ref_mad_normalized,
ac_relative_importance = ac_importance / ref_ac_importance
)
}
)
) |>
select(-baseline_loo)
results_long <- rel_simulation_structure |>
tidyr::unnest(loo_results) |>
# enforce one value per replicate (if already unique, no change)
dplyr::group_by(replicate, variable, method) |>
dplyr::summarise(
dplyr::across(
c(mad_importance, cc_importance, ac_importance,
mad_normalized, mad_relative_importance, ac_relative_importance),
~ mean(.x, na.rm = TRUE)
),
.groups = "drop"
)
results_summary <- results_long |>
dplyr::group_by(variable, method) |>
dplyr::summarise(
dplyr::across(
c(mad_importance, cc_importance, ac_importance,
mad_normalized, mad_relative_importance, ac_relative_importance),
list(
mean = \(x) mean(x, na.rm = TRUE),
sd = \(x) sd(x, na.rm = TRUE)
),
.names = "{.col}_{.fn}"
),
.groups = "drop"
)
results_wide <- results_summary |>
tidyr::pivot_wider(
names_from = method,
values_from = -c(variable, method)
)
measure_names <- c(
"mad_importance",
"cc_importance",
"ac_importance",
"mad_normalized",
"mad_relative_importance",
"ac_relative_importance"
)
split_by_measure_mean <- purrr::map(
measure_names,
\(measure) {
results_wide |>
dplyr::select(variable, dplyr::starts_with(paste0(measure, "_mean_"))) |>
dplyr::rename_with(
~ stringr::str_remove(., paste0(measure, "_mean_")),
-variable
)
}
) |> rlang::set_names(measure_names)
split_by_measure_sd <- purrr::map(
measure_names,
\(measure) {
results_wide |>
dplyr::select(variable, dplyr::starts_with(paste0(measure, "_sd_"))) |>
dplyr::rename_with(
~ stringr::str_remove(., paste0(measure, "_sd_")),
-variable
)
}
) |> rlang::set_names(measure_names)
```
### Code for `Figure 1`
```{r,fig.height=5,fig.width=8}
meas_to_plot_mad_mean <- split_by_measure_mean |> pluck("mad_importance") |>
mutate(measure="mad_importance") |> slice(3:6,1,2) |> mutate(var_id=1:6)
meas_to_plot_mad_sd <- split_by_measure_sd |> pluck("mad_importance") |>
mutate(measure="mad_importance") |> slice(3:6,1,2) |> mutate(var_id=1:6)
mad_max <- max(meas_to_plot_mad_mean |> select(where(is.numeric), -var_id), na.rm = TRUE)
rect_data <- tibble(
xmin_cont=4.5,xmax_cont=6,ymin_cont=0,ymax_cont=mad_max,
xmin_cat=.5,xmax_cat=4.5,ymin_cat=0,ymax_cat=mad_max
)
meas_to_plot_mad_rel_mean <- split_by_measure_mean |> pluck("mad_normalized") |>
mutate(measure="mad_normalized") |> slice(3:6,1,2) |> mutate(var_id=1:6)
meas_to_plot_mad_rel_sd <- split_by_measure_sd |> pluck("mad_normalized") |>
mutate(measure="mad_normalized") |> slice(3:6,1,2) |> mutate(var_id=1:6)
mad_max_rel <- max(meas_to_plot_mad_rel_mean |> select(where(is.numeric), -var_id), na.rm = TRUE)
rect_data_rel <- tibble(
xmin_cont=4.5,xmax_cont=6,ymin_cont=0,ymax_cont=mad_max_rel,
xmin_cat=.5,xmax_cat=4.5,ymin_cat=0,ymax_cat=mad_max_rel
)
loo_mad_plot <- meas_to_plot_mad_mean |>
canon_cols() |>
dplyr::select(variable, var_id, any_of(method_levels)) |>
pivot_longer(cols = naive:u_mix, names_to="method", values_to="value") |>
mutate(
method = factor(method, levels = method_levels),
additive = ifelse(method %in% c("gower","mod_gower","hl_add","u_ind","u_dep","u_mix"),
"additive distances", "non-additive distances")
) |>
dplyr::left_join(
meas_to_plot_mad_sd |>
canon_cols() |>
dplyr::select(variable, var_id, any_of(method_levels)) |>
pivot_longer(cols = naive:u_mix, names_to="method", values_to="sd") |>
mutate(method = factor(method, levels = method_levels)),
by = c("variable","var_id","method")
) |>
ggplot(aes(x = var_id, y = value, color = method, shape = method)) +
geom_rect(data=rect_data,
aes(xmin=xmin_cont,xmax=xmax_cont,ymin=ymin_cont,ymax=ymax_cont),
alpha=.2, fill="indianred", color="lightgrey", inherit.aes=FALSE) +
geom_rect(data=rect_data,
aes(xmin=xmin_cat,xmax=xmax_cat,ymin=ymin_cat,ymax=ymax_cat),
alpha=.2, fill="dodgerblue", color="lightgrey", inherit.aes=FALSE) +
geom_errorbar(aes(ymin = value - sd, ymax = value + sd), width = 0.12, linewidth = 0.35) +
geom_point() + geom_line() +
ylab("absolute variable contribution to distance") +
xlab("") + theme_bw() + theme(legend.position = "none") +
scale_x_continuous(breaks=seq(1,6,1), labels = rep("",6)) +
theme(axis.text.x = element_text(angle = 60, hjust = 1)) +
scale_shape_manual(values = my_shapes) +
scale_color_manual(values = my_colors) +
facet_wrap(.~additive)
add_methods <- c("gower","mod_gower","hl_add","u_ind","u_dep","u_mix")
nonadd_methods <- c("naive","hl","gudmm","dkps")
# add_methods <- c("gower", "mod_gower", "hl_add", "u_ind", "u_dep", "u_mix")
legend_breaks <- c(
c("gower","mod_gower","hl_add","u_ind","u_dep","u_mix"), # additive first
c("naive","hl","gudmm","dkps") # non-additive after
)
legend_labels <- setNames(
ifelse(legend_breaks %in% c("gower","mod_gower","hl_add","u_ind","u_dep","u_mix"),
paste0(legend_breaks, " (additive)"),
paste0(legend_breaks, " (non-additive)")),
legend_breaks
)
library(ggnewscale)
loo_mad_rel_df <- meas_to_plot_mad_rel_mean |>
canon_cols() |>
dplyr::select(variable, var_id, any_of(method_levels)) |>
tidyr::pivot_longer(cols = naive:u_mix, names_to="method", values_to="value") |>
mutate(
method = factor(method, levels = c("naive","hl","hl_add","gower","gudmm","dkps","mod_gower","u_ind","u_dep","u_mix")),
additive = ifelse(as.character(method) %in% add_methods, "additive", "non-additive")
) |>
dplyr::left_join(
meas_to_plot_mad_rel_sd |>
canon_cols() |>
dplyr::select(variable, var_id, any_of(method_levels)) |>
tidyr::pivot_longer(cols = naive:u_mix, names_to="method", values_to="sd") |>
mutate(method = factor(method, levels = c("naive","hl","hl_add","gower","gudmm","dkps","mod_gower","u_ind","u_dep","u_mix"))),
by = c("variable","var_id","method")
)
loo_mad_rel_plot <-
ggplot() +
geom_rect(data=rect_data_rel,
aes(xmin=xmin_cont,xmax=xmax_cont,ymin=ymin_cont,ymax=ymax_cont),
alpha=.2, fill="indianred", color="lightgrey", inherit.aes=FALSE) +
geom_rect(data=rect_data_rel,
aes(xmin=xmin_cat,xmax=xmax_cat,ymin=ymin_cat,ymax=ymax_cat),
alpha=.2, fill="dodgerblue", color="lightgrey", inherit.aes=FALSE) +
# --- Additive layer + legend 1 ---
# geom_errorbar(
# data = dplyr::filter(loo_mad_rel_df, additive == "additive"),
# aes(x = var_id, ymin = value - sd, ymax = value + sd, color = method),
# width = 0.12, linewidth = 0.35
# ) +
geom_line(
data = dplyr::filter(loo_mad_rel_df, additive == "additive"),
aes(x = var_id, y = value, color = method)
) +
geom_point(
data = dplyr::filter(loo_mad_rel_df, additive == "additive"),
aes(x = var_id, y = value, color = method, shape = method)
) +
scale_color_manual(
name = "additive",
values = my_colors,
breaks = add_methods
) +
scale_shape_manual(
name = "additive",
values = my_shapes,
breaks = add_methods
) +
guides(
color = guide_legend(
order = 1,
override.aes = list(shape = my_shapes[add_methods])
),
shape = "none"
) +
ggnewscale::new_scale_color() +
ggnewscale::new_scale("shape") +
# --- Non-additive layer + legend 2 ---
# geom_errorbar(
# data = dplyr::filter(loo_mad_rel_df, additive == "non-additive"),
# aes(x = var_id, ymin = value - sd, ymax = value + sd, color = method),
# width = 0.12, linewidth = 0.35
# ) +
geom_line(
data = dplyr::filter(loo_mad_rel_df, additive == "non-additive"),
aes(x = var_id, y = value, color = method)
) +
geom_point(
data = dplyr::filter(loo_mad_rel_df, additive == "non-additive"),
aes(x = var_id, y = value, color = method, shape = method)
) +
scale_color_manual(
name = "non-additive",
values = my_colors,
breaks = nonadd_methods
) +
scale_shape_manual(
name = "non-additive",
values = my_shapes,
breaks = nonadd_methods
) +
guides(
color = guide_legend(
order = 2,
override.aes = list(shape = my_shapes[nonadd_methods])
),
shape = "none"
) +
# cosmetics (same as yours)
ylab("relative variable contribution to distance") +
xlab("left-out variable") + theme_bw() +
scale_x_continuous(
breaks=seq(1,6,1),
labels = c("2 cats", "3 cats", "5 cats", "9 cats", "num 1", "num 2")
) +
theme(
axis.text.x = element_text(angle = 60, hjust = 1),
strip.text = element_blank(),
legend.position = "bottom",
legend.title.position = "top",
legend.text = element_text(size = 13)
)+facet_wrap(.~additive)
fig_1_plot = loo_mad_plot / loo_mad_rel_plot
fig_1_plot
```
```{r, eval = FALSE, echo = FALSE}
ggsave(fig_1_plot, file = "figure_1_mad_importances.pdf", width = 8, height = 8)
```
### Code for `Figure 2`
```{r,fig.height=4,fig.width=8}
library(ggnewscale)
add_methods <- c("gower","mod_gower","hl_add","u_ind","u_dep","u_mix")
nonadd_methods <- c("naive","hl","gudmm","dkps")
meas_to_plot_ac_mean <- split_by_measure_mean |> pluck("ac_relative_importance") |>
mutate(measure="ac_relative_importance") |> slice(3:6,1,2) |> mutate(var_id=1:6)
meas_to_plot_ac_sd <- split_by_measure_sd |> pluck("ac_relative_importance") |>
mutate(measure="ac_relative_importance") |> slice(3:6,1,2) |> mutate(var_id=1:6)
ac_max <- max(meas_to_plot_ac_mean |> select(where(is.numeric), -var_id), na.rm = TRUE)
rect_data_ac <- tibble(
xmin_cont=4.5,xmax_cont=6,ymin_cont=0,ymax_cont=ac_max,
xmin_cat=.5,xmax_cat=4.5,ymin_cat=0,ymax_cat=ac_max
)
ac_df <- meas_to_plot_ac_mean |>
canon_cols() |>
dplyr::select(variable, var_id, any_of(method_levels)) |>
tidyr::pivot_longer(cols = naive:u_mix, names_to="method", values_to="value") |>
mutate(
method = factor(method, levels = c("naive","hl","hl_add","gower","gudmm","dkps","mod_gower","u_ind","u_dep","u_mix")),
additive = ifelse(as.character(method) %in% add_methods, "additive", "non-additive")
) |>
dplyr::left_join(
meas_to_plot_ac_sd |>
canon_cols() |>
dplyr::select(variable, var_id, any_of(method_levels)) |>
tidyr::pivot_longer(cols = naive:u_mix, names_to="method", values_to="sd") |>
mutate(method = factor(method, levels = c("naive","hl","hl_add","gower","gudmm","dkps","mod_gower","u_ind","u_dep","u_mix"))),
by = c("variable","var_id","method")
)
ac_plot <-
ggplot() +
geom_rect(data=rect_data_ac,
aes(xmin=xmin_cont,xmax=xmax_cont,ymin=ymin_cont,ymax=ymax_cont),
alpha=.2, fill="indianred", color="lightgrey", inherit.aes=FALSE) +
geom_rect(data=rect_data_ac,
aes(xmin=xmin_cat,xmax=xmax_cat,ymin=ymin_cat,ymax=ymax_cat),
alpha=.2, fill="dodgerblue", color="lightgrey", inherit.aes=FALSE) +
# --- Additive legend (left / first) ---
geom_line(
data = dplyr::filter(ac_df, additive == "additive"),
aes(x = var_id, y = value, color = method)
) +
geom_point(
data = dplyr::filter(ac_df, additive == "additive"),
aes(x = var_id, y = value, color = method, shape = method)
) +
scale_color_manual(name = "additive", values = my_colors, breaks = add_methods) +
scale_shape_manual(name = "additive", values = my_shapes, breaks = add_methods) +
guides(
color = guide_legend(order = 1, override.aes = list(shape = my_shapes[add_methods])),
shape = "none"
) +
ggnewscale::new_scale_color() +
ggnewscale::new_scale("shape") +
# --- Non-additive legend (right / second) ---
geom_line(
data = dplyr::filter(ac_df, additive == "non-additive"),
aes(x = var_id, y = value, color = method)
) +
geom_point(
data = dplyr::filter(ac_df, additive == "non-additive"),
aes(x = var_id, y = value, color = method, shape = method)
) +
scale_color_manual(name = "non-additive", values = my_colors, breaks = nonadd_methods) +
scale_shape_manual(name = "non-additive", values = my_shapes, breaks = nonadd_methods) +
guides(
color = guide_legend(order = 2, override.aes = list(shape = my_shapes[nonadd_methods])),
shape = "none"
) +
# cosmetics
ylab("relative alienation coefficient") +
xlab("left-out variable") +
scale_x_continuous(
breaks=seq(1,6,1),
labels = c("2 cats", "3 cats", "5 cats", "9 cats", "num 1", "num 2")
) +
theme_bw() +
theme(
axis.text.x = element_text(angle = 60, hjust = 1),
legend.position = "bottom",
legend.title.position = "top",
legend.text = element_text(size = 13)
)+ facet_wrap(.~additive)
ac_plot
```
```{r, echo=FALSE,eval=FALSE}
ggsave("figure_2_ac_importances.pdf", ac_plot, width = 8, height = 4)
```
## Retrieval of the true configuration
### Data generation
```{r, eval=FALSE}
recovery_structure <- tidyr::crossing(
tibble::tibble(replicate = 1:reps),
method = methods,
categories = qoptions
) |>
dplyr::left_join(manydist:::mdist_method_lookup, by = "method") |>
dplyr::mutate(
dataset = purrr::map2(
.x = replicate, .y = categories,
~ generate_dataset(
n = n, porig = porig, pn = pn,
pnnoise = pnnoise, pcnoise = pcnoise,
sigma = sigma, qoptions = .y, mode = "shared",
seed = 1234 + .x
)
),
# compute distance matrix using method specs + baseline uses Xorig
distance_matrix = purrr::pmap(
dplyr::pick(dataset, method, mdist_type, mdist_preset, param_set),
\(dataset, method, mdist_type, mdist_preset, param_set) {
X <- if (method == "baseline") dataset$Xorig else dataset$X
run_mdist_within(
df = X,
mdist_type = mdist_type,
mdist_preset = mdist_preset,
param_set = param_set,
outcome = NULL # because X / Xorig have no response column
) |>
base::as.matrix()
}
),
mds_results = purrr::map(
distance_matrix,
~ cmdscale(.x, eig = TRUE, k = 2)$points |>
as.data.frame() |>
setNames(c("x1", "x2"))
),
congruence_coeff = purrr::map2(
.x = mds_results, .y = dataset,
\(mds, ds) congruence_coeff(ds$truth, mds)
)
)
# save(file="recovery_structure.RData", recovery_structure)
recovery_structure_lite = recovery_structure |>
select(-dataset, -distance_matrix, -mds_results) |>
unnest(congruence_coeff) |>
select(replicate, method, categories, congruence_coeff) |>
mutate(categories=factor(paste0(categories," categories")),
alienation_coeff = sqrt(1-congruence_coeff^2))
save(file="recovery_structure_lite.RData", recovery_structure_lite)
```
### Code for figure `Figure 3`
```{r,echo=FALSE}
load("recovery_structure_lite.RData")
```
```{r,fig.height=8,fig.width=8}
library(dplyr)
library(ggplot2)
library(ggnewscale)
# n_add <- length(add_methods)
add_methods <- c("gower","mod_gower","hl_add","u_ind","u_dep","u_mix")
nonadd_methods <- c("naive","hl","gudmm","dkps")
method_order <- c(add_methods, nonadd_methods, "baseline")
n_add <- length(add_methods)
n_nonadd <- length(nonadd_methods)
n_total <- length(method_order)
rect_bg <- tibble::tibble(
xmin = c(0.5, n_add + 0.5),
xmax = c(n_add + 0.5, n_add + n_nonadd + 0.5),
ymin = c(-Inf, -Inf),
ymax = c( Inf, Inf),
grp = c("additive", "non-additive")
)
# --- method groups ---
# x-axis order: additive first, then non-additive, baseline last
# --- prepare data ---
box_df <- recovery_structure_lite |>
mutate(
method = ifelse(is.na(method), "baseline", method),
method = canon_method(method), # paper naming
method = factor(method, levels = method_order),
additive = ifelse(as.character(method) %in% add_methods, "additive", "non-additive")
)
# --- plot ---
boxplot_figure_simu <-
ggplot(box_df, aes(x = method, y = alienation_coeff)) +
geom_rect(
data = dplyr::filter(rect_bg, grp == "additive"),
aes(xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax),
inherit.aes = FALSE,
alpha = 0.20, fill = "dodgerblue", color = "lightgrey"
) +
geom_rect(
data = dplyr::filter(rect_bg, grp == "non-additive"),
aes(xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax),
inherit.aes = FALSE,
alpha = 0.20, fill = "indianred", color = "lightgrey"
) +
facet_wrap(~ categories) +
theme_bw() +
theme(
axis.text.x = element_text(angle = 60, hjust = 1),
legend.position = "bottom",
legend.title.position = "top",
legend.text = element_text(size = 13)
) +
ylab("alienation coefficient") +
xlab("methods") +
# --- additive boxes + legend 1 (left) ---
geom_boxplot(
data = dplyr::filter(box_df, additive == "additive"),
aes(fill = method),
outlier.alpha = 0.25,
linewidth = 0.35
) +
scale_fill_manual(
name = "additive",
values = my_colors,
breaks = add_methods
) +
guides(fill = guide_legend(order = 1)) +
ggnewscale::new_scale_fill() +
# --- non-additive boxes (incl baseline) + legend 2 (right) ---
geom_boxplot(
data = dplyr::filter(box_df, additive == "non-additive"),
aes(fill = method),
outlier.alpha = 0.25,
linewidth = 0.35
) +
scale_fill_manual(
name = "non-additive",
values = my_colors,
breaks = c(nonadd_methods, "baseline") # baseline included here; appears last in x-axis
) +
guides(fill = guide_legend(order = 2))
boxplot_figure_simu
```
```{r,echo=FALSE, eval=FALSE}
ggsave(file="AC_boxplots.pdf",boxplot_figure_simu,width=8.5,height=6)
```
## Clustering experiment: partitioning around medoids
### numsep =.1 and catsep=0.35 generation
```{r, echo=TRUE,eval=FALSE}
nrep <- 100
k_true <- 4
q <- 9
numsep <- 0.1
catsep <- 0.35
clustSizeEq <- 50
param_generator_grid <- tibble::tibble(
numsignal = c(0,0,4,4,4,8,8,8),
numnoise = c(8,8,4,4,4,0,0,0),
catsignal = c(4,8,0,4,8,0,4,8),
catnoise = c(4,0,8,4,0,8,4,0)
) |>
tidyr::crossing(replicate = 1:nrep)
mixed_datasets_grid <- param_generator_grid |>
dplyr::mutate(
data = purrr::pmap(
dplyr::pick(numsignal, catsignal, numnoise, catnoise, replicate),
\(numsignal, catsignal, numnoise, catnoise, replicate) {
gen_mixed(
k_true = k_true,
clustSizeEq = clustSizeEq,
numsignal = numsignal,
numnoise = numnoise,
catsignal = catsignal,
catnoise = catnoise,
q = q,
q_err = q,
numsep = numsep,
catsep = catsep,
seed = replicate
)
}
)
)
methods <- c("naive","hl","hl_add","gower","gudmm","dkss","mod_gower","u_ind","u_dep","u_mix")
sim_methods_grid <- mixed_datasets_grid |>
tidyr::crossing(method = methods) |>
dplyr::left_join(manydist:::mdist_method_lookup, by = "method")
stopifnot(!any(is.na(sim_methods_grid$mdist_type)))
ari_pam_results_01_035 <- sim_methods_grid |>
dplyr::mutate(
ari = purrr::pmap_dbl(
dplyr::pick(data, mdist_type, mdist_preset, param_set),
\(data, mdist_type, mdist_preset, param_set) {
df <- data$df
D <- run_mdist_within(df, mdist_type, mdist_preset, param_set, outcome = "y")
pam_fit <- cluster::pam(D, k = k_true, diss = TRUE)
mclust::adjustedRandIndex(df$y, pam_fit$clustering)
}
)
)
```
```{r, echo=FALSE,eval=FALSE}
save(ari_pam_results_01_035, file = "ari_pam_experiment_numsep_01_catsep_035.RData")
```
```{r, echo=FALSE,eval=TRUE}
load(file = "ari_pam_experiment_numsep_01_catsep_035.RData")
```
```{r}
# Method groups (as you provided)
add_methods <- c("gower","mod_gower","hl_add","u_ind","u_dep","u_mix")
nonadd_methods <- c("naive","hl","gudmm","dkps")
method_levels <- c(add_methods, nonadd_methods)
# Facet order (row-wise)
scenario_order <- c("0844","0880","4408","8008","4444","4480","8044","8080")
ari_plot_df_01_035 <- ari_pam_results_01_035 |>
mutate(
# Used only to match facet order; preserves leading zeros
scenario_id = sprintf("%01d%01d%01d%01d", numsignal, numnoise, catsignal, catnoise),
scenario = str_glue(
"num: {numsignal} s. + {numnoise} n. | cat: {catsignal} s. + {catnoise} n."
),
method = canon_method(method),
# Row-wise facet order as provided
scenario = factor(scenario, levels = scenario[match(scenario_order, scenario_id)]),
# Method order
method = factor(method, levels = method_levels),
# Additive / Non-additive label
method_type = if_else(as.character(method) %in% add_methods, "Additive", "Non-additive")
)
# Background bands (no fill scale consumed)
k_add <- length(add_methods)
k_tot <- length(method_levels)
bg_add <- tibble(
xmin = 0.5, xmax = k_add + 0.5,
ymin = -Inf, ymax = Inf
)
bg_nonadd <- tibble(
xmin = k_add + 0.5, xmax = k_tot + 0.5,
ymin = -Inf, ymax = Inf
)
ari_plot_01_035 <- ggplot() +
# Shaded regions
geom_rect(
data = bg_add,
aes(xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax),
inherit.aes = FALSE,
fill = "indianred",
alpha = 0.12,
show.legend = FALSE
) +
geom_rect(
data = bg_nonadd,
aes(xmin = xmin, xmax = xmax, ymin = ymin, ymax = ymax),
inherit.aes = FALSE,
fill = "dodgerblue",
alpha = 0.12,
show.legend = FALSE
) +
# Additive boxplots + legend block
geom_boxplot(
data = ari_plot_df_01_035 |> filter(method_type == "Additive"),
aes(x = method, y = ari, fill = method),
outlier.alpha = 0.25,
linewidth = 0.35
) +
# Additive legend (comes first)
scale_fill_manual(
name = "Additive",
values = my_colors[add_methods],
breaks = add_methods,
drop = FALSE,
guide = guide_legend(order = 1)
) +
ggnewscale::new_scale_fill() +
# Non-additive boxplots + legend block
geom_boxplot(
data = ari_plot_df_01_035 |> filter(method_type == "Non-additive"),
aes(x = method, y = ari, fill = method),
outlier.alpha = 0.25,
linewidth = 0.35
) +
# Non-additive legend (comes second)
scale_fill_manual(
name = "Non-additive",
values = my_colors[nonadd_methods],
breaks = nonadd_methods,
drop = FALSE,
guide = guide_legend(order = 2)
) +
facet_wrap(~ scenario, ncol = 2) +
coord_cartesian(ylim = c(0, 1)) +
theme_bw() +
theme(
axis.text.x = element_text(angle = 60, hjust = 1),
strip.text = element_text(size = 9),
legend.text = element_text(size = 13)
) +
labs(x = "", y = "ARI (PAM on dissimilarities)")
print(ari_plot_01_035)
```
```{r,echo=FALSE,eval=FALSE}
ggsave(file = "ari_plot_01_035.pdf", ari_plot_01_035, width = 6, height = 8)
```
```{r,echo=FALSE}
load(file = "ari_pam_experiment_numsep_01_catsep_035.RData")
```
```{r}
# ---- method groups ----
add_methods <- c("gower","mod_gower","hl_add","u_ind","u_dep","u_mix")
nonadd_methods <- c("naive","hl","gudmm","dkps")
# ---- scenario order (shared with boxplot figure) ----
scenario_order <- c("0844","0880","4408","8008","4444","4480","8044","8080")
ari_parallel_df <- ari_pam_results_01_035 |>
mutate(
# unify method naming
method = canon_method(method),
# key used for ordering
scenario_id = sprintf(
"%01d%01d%01d%01d",
numsignal, numnoise, catsignal, catnoise
),
# label shown on the x-axis
scenario = stringr::str_glue(
"n:({numsignal},{numnoise}); c:({catsignal},{catnoise})"
)
) |>
group_by(scenario_id, scenario, method) |>
summarise(
mean_ari = mean(ari, na.rm = TRUE),
sd_ari = sd(ari, na.rm = TRUE),
.groups = "drop"
) |>
mutate(
# enforce scenario order explicitly
scenario = factor(
scenario,
levels = scenario[match(scenario_order, scenario_id)]
),
type = ifelse(method %in% add_methods, "additive", "non-additive"),
method = factor(method, levels = c(add_methods, nonadd_methods))
)
```
### Code for `Figure 4`
```{r}
ari_parallel_plot <-
ggplot() +
# ================= ADDITIVE =================
geom_errorbar(
data = dplyr::filter(ari_parallel_df, type == "additive"),
aes(
x = scenario,
ymin = mean_ari - sd_ari,
ymax = mean_ari + sd_ari,
color = method
),
width = 0.12,
linewidth = 0.35
) +
geom_line(
data = dplyr::filter(ari_parallel_df, type == "additive"),
aes(x = scenario, y = mean_ari, color = method, group = method),
linewidth = 0.6,alpha=.75
) +
geom_point(
data = dplyr::filter(ari_parallel_df, type == "additive"),
aes(x = scenario, y = mean_ari, color = method, shape = method),
size = 2
) +
scale_color_manual(name = "additive", values = my_colors, breaks = add_methods) +
scale_shape_manual(name = "additive", values = my_shapes, breaks = add_methods) +
guides(
color = guide_legend(order = 1, override.aes = list(shape = my_shapes[add_methods])),
shape = "none"
) +
ggnewscale::new_scale_color() +
ggnewscale::new_scale("shape") +
# ================= NON-ADDITIVE =================
geom_errorbar(
data = dplyr::filter(ari_parallel_df, type == "non-additive"),
aes(
x = scenario,
ymin = mean_ari - sd_ari,
ymax = mean_ari + sd_ari,
color = method
),
width = 0.12,
linewidth = 0.35
) +
geom_line(
data = dplyr::filter(ari_parallel_df, type == "non-additive"),
aes(x = scenario, y = mean_ari, color = method, group = method),
linewidth = 0.6,alpha=.75
) +
geom_point(
data = dplyr::filter(ari_parallel_df, type == "non-additive"),
aes(x = scenario, y = mean_ari, color = method, shape = method),
size = 2
) +
scale_color_manual(name = "non-additive", values = my_colors, breaks = nonadd_methods) +
scale_shape_manual(name = "non-additive", values = my_shapes, breaks = nonadd_methods) +
guides(
color = guide_legend(order = 2, override.aes = list(shape = my_shapes[nonadd_methods])),
shape = "none"
) +
labs(x = "scenario", y = "mean ARI (± 1 SD)") +
theme_bw() +
theme(
axis.text.x = element_text(angle = 30, hjust = 1),
legend.position = "bottom",
legend.title.position = "top",
legend.text = element_text(size = 13)
)
ari_parallel_plot
ggsave(
filename = "figure_parallel_ari.pdf",
plot = ari_parallel_plot,
width = 18,
height = 11,
units = "cm"
)
```
<!-- ## rankings -->
```{r}
load(file = "ari_pam_experiment_numsep_01_catsep_035.RData")
add_methods <- c("gower","mod_gower","hl_add","u_ind","u_dep","u_mix")
nonadd_methods <- c("naive","hl","gudmm","dkps")
scenario_order <- c("0844","0880","4408","8008","4444","4480","8044","8080")
ari_rank_df <- ari_pam_results_01_035 |>
mutate(
method = canon_method(method),
scenario_id = sprintf("%01d%01d%01d%01d", numsignal, numnoise, catsignal, catnoise),
scenario = stringr::str_glue("n:({numsignal},{numnoise}); c:({catsignal},{catnoise})")
) |>
group_by(scenario_id, scenario, method) |>
summarise(
mean_ari = mean(ari, na.rm = TRUE),
.groups = "drop"
) |>
group_by(scenario_id, scenario) |>
mutate(
rank_desc = dplyr::dense_rank(dplyr::desc(mean_ari)) # 1 = best
) |>
ungroup() |>
mutate(
# enforce scenario order (same as boxplot panels)
scenario = factor(scenario, levels = scenario[match(scenario_order, scenario_id)]),
type = ifelse(method %in% add_methods, "additive", "non-additive"),
method = factor(method, levels = c(add_methods, nonadd_methods))
)
```
<!-- ## Figure -->
<!-- ```{r} -->
<!-- K_methods <- max(ari_rank_df$rank_desc, na.rm = TRUE) -->
<!-- ari_parallel_rank_plot <- -->
<!-- ggplot() + -->
<!-- # ================= ADDITIVE ================= -->
<!-- geom_line( -->
<!-- data = dplyr::filter(ari_rank_df, type == "additive"), -->
<!-- aes(x = scenario, y = rank_desc, color = method, group = method), -->
<!-- linewidth = 0.6,alpha=.75 -->
<!-- ) + -->
<!-- geom_point( -->
<!-- data = dplyr::filter(ari_rank_df, type == "additive"), -->
<!-- aes(x = scenario, y = rank_desc, color = method, shape = method), -->
<!-- size = 2 -->
<!-- ) + -->
<!-- scale_color_manual(name = "additive", values = my_colors, breaks = add_methods) + -->
<!-- scale_shape_manual(name = "additive", values = my_shapes, breaks = add_methods) + -->
<!-- guides( -->
<!-- color = guide_legend(order = 1, -->
<!-- override.aes = list(shape = my_shapes[add_methods]) -->
<!-- ), -->
<!-- shape = "none" -->
<!-- ) + -->
<!-- ggnewscale::new_scale_color() + -->
<!-- ggnewscale::new_scale("shape") + -->
<!-- # ================= NON-ADDITIVE ================= -->
<!-- geom_line( -->
<!-- data = dplyr::filter(ari_rank_df, type == "non-additive"), -->
<!-- aes(x = scenario, y = rank_desc, color = method, group = method), -->
<!-- linewidth = 0.6,alpha=.75 -->
<!-- ) + -->
<!-- geom_point( -->
<!-- data = dplyr::filter(ari_rank_df, type == "non-additive"), -->
<!-- aes(x = scenario, y = rank_desc, color = method, shape = method), -->
<!-- size = 2 -->
<!-- ) + -->
<!-- scale_color_manual(name = "non-additive", values = my_colors, breaks = nonadd_methods) + -->
<!-- scale_shape_manual(name = "non-additive", values = my_shapes, breaks = nonadd_methods) + -->
<!-- guides( -->
<!-- color = guide_legend(order = 2, -->
<!-- override.aes = list(shape = my_shapes[nonadd_methods]) -->
<!-- ), -->
<!-- shape = "none" -->
<!-- ) + -->
<!-- # ---- THIS IS THE KEY LINE ---- -->
<!-- scale_y_reverse( -->
<!-- breaks = 1:K_methods, -->
<!-- limits = c(K_methods, 1) -->
<!-- ) + -->
<!-- labs( -->
<!-- x = "scenario", -->
<!-- y = "rank of mean ARI (1 = best)" -->
<!-- ) + -->
<!-- theme_bw() + -->
<!-- theme( -->
<!-- axis.text.x = element_text(angle = 30, hjust = 1), -->
<!-- legend.position = "bottom", -->
<!-- legend.title.position = "top", -->
<!-- legend.text = element_text(size = 13) -->
<!-- ) -->
<!-- ari_parallel_rank_plot -->
<!-- ggsave( -->
<!-- filename = "figure_parallel_rank.pdf", -->
<!-- plot = ari_parallel_rank_plot, -->
<!-- width = 18, -->
<!-- height = 11, -->
<!-- units = "cm" -->
<!-- ) -->
<!-- ``` -->
## Illustration: FIFA player data
### Data preparation and analysis
```{r, eval=FALSE}
# Variables are organized: Categorical first, then numerical
data("fifa_nl", package = "manydist")
#Xorig<-X<-ddata[,-c(1,2)]
X<-fifa_nl[,-c(1,2,19:24)] # vars 1 and 2 are a bit useless (too many categories)
# vars 19:24 interesting but same scale and little variation
# leaving them out makes the plots a bit smaller.
# leaving them in doesn't seem to change a lot
n<-nrow(X)
nd<-2 # Dimensionality of MDS solution
X=X[,c(8:1,9:16)] # Order
X=X[,-3] # Remove int rep: 380 have something, 21+7 in other cats
X=X[,c(1:12,14,13,15)]
p<-ncol(X)
X[8:15] <- lapply(X[8:15], as.numeric)
fifa_clean <- as_tibble(X) |>
select(where(is.integer), where(is.numeric),where(is.factor) ,-release_clause_eur) |>
rename(pref_foot=`preferred_foot`,
club=`club_name`,
position=`team_position`)
```
```{r, eval=FALSE}
fifa_structure <- tibble::tibble(
method = c("naive","hl","hl_add","gower","gudmm","dkss","mod_gower","u_ind","u_dep","u_mix")
) |>
dplyr::left_join(manydist:::mdist_method_lookup, by = "method") |>
dplyr::mutate(
loo_results = purrr::pmap(
dplyr::pick(method, mdist_type, mdist_preset, param_set),
\(method, mdist_type, mdist_preset, param_set) {
run_lovo(
df = fifa_clean,
mdist_type = mdist_type,
mdist_preset = mdist_preset,
param_set = param_set,
outcome = NULL,
dims = nd,
keep_dist = FALSE,
legacy_gower_sum = (method == "gower") # triggers only for preset+gower anyway
)
}
)
)
```
```{r, eval=FALSE,echo=FALSE}
save(file="fifa_structure_R3.RData", fifa_structure)
```
```{r, echo = FALSE}
load("fifa_structure_R3.RData")
```
```{r}
results_fifa_wide <- fifa_structure |>
dplyr::mutate(loo_tbl = purrr::map(loo_results, "results")) |>
dplyr::select(method, loo_tbl) |>
tidyr::unnest(loo_tbl) |>
tidyr::pivot_wider(
id_cols = variable,
names_from = method,
values_from = c(mad_importance, cc_importance, ac_importance, mad_normalized)
)
measure_names <- c(
"mad_importance",
"cc_importance",
"ac_importance",
"mad_normalized"
)
fifa_split_by_measure <- purrr::map(
measure_names,
\(measure) {
results_fifa_wide |>
dplyr::select(variable, dplyr::starts_with(paste0(measure, "_"))) |>
dplyr::rename_with(~ stringr::str_remove(.x, paste0(measure, "_")))
}
) |>
rlang::set_names(measure_names)
```
### Code for `Figure 5`
```{r,fig.height=5,fig.width=8}
meas_to_plot_mad = fifa_split_by_measure |> pluck("mad_importance") |>
mutate(measure="mad_importances") |> slice(c(8:14,1:7)) |> mutate(var_id=1:n())
mad_max = max(meas_to_plot_mad |> select(where(is.numeric),-var_id))
rect_data = tibble(
xmin_cont=8.5,xmax_cont=14,ymin_cont=0,ymax_cont=mad_max,
xmin_cat=.5,xmax_cat=8.5,ymin_cat=0,ymax_cat=mad_max)
meas_to_plot_mad_rel = fifa_split_by_measure |> pluck("mad_normalized") |>
mutate(measure="mad_normalized")|> slice(c(8:14,1:7)) |> mutate(var_id=1:n())
mad_max_rel = max(meas_to_plot_mad_rel |> select(where(is.numeric),-var_id))
rect_data_rel = tibble(
xmin_cont=8.5,xmax_cont=14,ymin_cont=0,ymax_cont=mad_max_rel,
xmin_cat=.5,xmax_cat=8.5,ymin_cat=0,ymax_cat=mad_max_rel)
# --- DROP-IN: Figure 4 (MAD importances) with split legend (shown only on bottom plot) ---
method_levels <- c("naive","hl","hl_add","gower","gudmm","dkps","mod_gower","u_ind","u_dep","u_mix")
additive_set <- c("gower","mod_gower","hl_add","u_ind","u_dep","u_mix")
conflict_prefer("intersect", "base")
conflict_prefer("setdiff", "base")
add_present <- intersect(additive_set, method_levels)
nonadd_present <- setdiff(method_levels, additive_set)
# ---------- TOP: absolute contributions ----------
loo_mad_long <- meas_to_plot_mad |>
canon_cols() |>
pivot_longer(
cols = any_of(method_levels),
names_to = "method",
values_to = "value"
) |>
mutate(
method = factor(method, levels = method_levels),
additive = ifelse(method %in% additive_set, "additive distances", "non-additive distances"),
type = ifelse(method %in% additive_set, "Additive", "Non-additive")
)
loo_mad_plot <-
ggplot() +
geom_rect(
data = rect_data,
aes(xmin = xmin_cont, xmax = xmax_cont, ymin = ymin_cont, ymax = ymax_cont),
alpha = .2, fill = "indianred", color = "lightgrey", inherit.aes = FALSE
) +
geom_rect(
data = rect_data,
aes(xmin = xmin_cat, xmax = xmax_cat, ymin = ymin_cat, ymax = ymax_cat),
alpha = .2, fill = "dodgerblue", color = "lightgrey", inherit.aes = FALSE
) +
# Additive
geom_line(
data = filter(loo_mad_long, type == "Additive"),
aes(x = var_id, y = value, color = method, group = method),
alpha = 0.85
) +
geom_point(
data = filter(loo_mad_long, type == "Additive"),
aes(x = var_id, y = value, color = method, shape = method),
size = 2
) +
scale_color_manual(
name = "Additive",
values = my_colors,
breaks = add_present,
drop = FALSE,
guide = guide_legend(order = 1, override.aes = list(shape = my_shapes[add_present]))
) +
scale_shape_manual(
name = "Additive",
values = my_shapes,
breaks = add_present,
drop = FALSE
) +
guides(shape = "none") +
ggnewscale::new_scale_color() +
ggnewscale::new_scale("shape") +
# Non-additive
geom_line(
data = filter(loo_mad_long, type == "Non-additive"),
aes(x = var_id, y = value, color = method, group = method),
alpha = 0.85
) +
geom_point(
data = filter(loo_mad_long, type == "Non-additive"),
aes(x = var_id, y = value, color = method, shape = method),
size = 2
) +
scale_color_manual(
name = "Non-additive",
values = my_colors,
breaks = nonadd_present,
drop = FALSE,
guide = guide_legend(order = 2, override.aes = list(shape = my_shapes[nonadd_present]))
) +
scale_shape_manual(
name = "Non-additive",
values = my_shapes,
breaks = nonadd_present,
drop = FALSE
) +
guides(shape = "none") +
ylab("absolute variable contribution to distance") +
theme_bw() +
scale_x_continuous(breaks = seq(1, 14, 1), labels = rep("", 14)) +
theme(
axis.text.x = element_text(angle = 60, hjust = 1),
legend.position = "none" # <-- keep legend hidden on TOP plot
) +
xlab("") +
facet_wrap(. ~ additive)
# ---------- BOTTOM: relative contributions ----------
loo_mad_rel_long <- meas_to_plot_mad_rel |>
canon_cols() |>
pivot_longer(
cols = any_of(method_levels),
names_to = "method",
values_to = "value"
) |>
mutate(
method = factor(method, levels = method_levels),
additive = ifelse(method %in% additive_set, "additive distances", "non-additive distances"),
type = ifelse(method %in% additive_set, "Additive", "Non-additive")
)
loo_mad_rel_plot <-
ggplot() +
geom_rect(
data = rect_data_rel,
aes(xmin = xmin_cont, xmax = xmax_cont, ymin = ymin_cont, ymax = ymax_cont),
alpha = .2, fill = "indianred", color = "lightgrey", inherit.aes = FALSE
) +
geom_rect(
data = rect_data_rel,
aes(xmin = xmin_cat, xmax = xmax_cat, ymin = ymin_cat, ymax = ymax_cat),
alpha = .2, fill = "dodgerblue", color = "lightgrey", inherit.aes = FALSE
) +
# Additive
geom_line(
data = filter(loo_mad_rel_long, type == "Additive"),
aes(x = var_id, y = value, color = method, group = method),
alpha = 0.85
) +
geom_point(
data = filter(loo_mad_rel_long, type == "Additive"),
aes(x = var_id, y = value, color = method, shape = method),
size = 2
) +
scale_color_manual(
name = "Additive",
values = my_colors,
breaks = add_present,
drop = FALSE,
guide = guide_legend(order = 1, override.aes = list(shape = my_shapes[add_present]))
) +
scale_shape_manual(
name = "Additive",
values = my_shapes,
breaks = add_present,
drop = FALSE
) +
guides(shape = "none") +
ggnewscale::new_scale_color() +
ggnewscale::new_scale("shape") +
# Non-additive
geom_line(
data = filter(loo_mad_rel_long, type == "Non-additive"),
aes(x = var_id, y = value, color = method, group = method),
alpha = 0.85
) +
geom_point(
data = filter(loo_mad_rel_long, type == "Non-additive"),
aes(x = var_id, y = value, color = method, shape = method),
size = 2
) +
scale_color_manual(
name = "Non-additive",
values = my_colors,
breaks = nonadd_present,
drop = FALSE,
guide = guide_legend(order = 2, override.aes = list(shape = my_shapes[nonadd_present]))
) +
scale_shape_manual(
name = "Non-additive",
values = my_shapes,
breaks = nonadd_present,
drop = FALSE
) +
guides(shape = "none") +
ylab("relative variable contribution to distance") +
theme_bw() +
scale_x_continuous(breaks = seq(1, 14, 1), labels = meas_to_plot_mad_rel$variable) +
theme(
axis.text.x = element_text(angle = 60, hjust = 1),
strip.text = element_blank(),
legend.position = "bottom",
legend.title.position = "top",
legend.text = element_text(size = 13)
) +
xlab("") +
facet_wrap(. ~ additive)
# ---------- COMBINE + SAVE ----------
fig_4_plot <- loo_mad_plot / loo_mad_rel_plot
fig_4_plot
```
```{r,echo=FALSE,eval=FALSE}
ggsave(fig_4_plot, file = "figure_4_mad_importances.pdf", width = 7, height = 7)
```
### Code for `Figure 6`
```{r,fig.height=5,fig.width=8}
method_levels <- c("naive","hl","hl_add","gower","gudmm","dkps","mod_gower","u_ind","u_dep","u_mix")
additive_set <- c("gower","mod_gower","hl_add","u_ind","u_dep","u_mix")
meas_to_plot_ac <- fifa_split_by_measure |>
purrr::pluck("ac_importance") |>
dplyr::mutate(measure = "ac_importance") |>
dplyr::slice(c(8:14, 1:7)) |>
dplyr::mutate(var_id = dplyr::row_number())
max_ac <- meas_to_plot_ac |>
dplyr::select(where(is.numeric), -var_id) |>
unlist(use.names = FALSE) |>
max(na.rm = TRUE)
rect_data_ac <- tibble::tibble(
xmin_cont = 7.5, xmax_cont = 14, ymin_cont = 0, ymax_cont = max_ac,
xmin_cat = 0.5, xmax_cat = 7.5, ymin_cat = 0, ymax_cat = max_ac
)
ac_long <- meas_to_plot_ac |>
canon_cols() |>
tidyr::pivot_longer(
cols = dplyr::any_of(method_levels),
names_to = "method",
values_to = "value"
) |>
dplyr::mutate(
method = factor(method, levels = method_levels),
additive = ifelse(method %in% additive_set, "additive distances", "non-additive distances"),
type = ifelse(method %in% additive_set, "Additive", "Non-additive")
)
add_present <- intersect(additive_set, unique(as.character(ac_long$method)))
nonadd_present <- intersect(setdiff(method_levels, additive_set), unique(as.character(ac_long$method)))
ac_plot <-
ggplot2::ggplot() +
ggplot2::geom_rect(
data = rect_data_ac,
ggplot2::aes(xmin = xmin_cont, xmax = xmax_cont, ymin = ymin_cont, ymax = ymax_cont),
alpha = .2, fill = "indianred", color = "lightgrey", inherit.aes = FALSE
) +
ggplot2::geom_rect(
data = rect_data_ac,
ggplot2::aes(xmin = xmin_cat, xmax = xmax_cat, ymin = ymin_cat, ymax = ymax_cat),
alpha = .2, fill = "dodgerblue", color = "lightgrey", inherit.aes = FALSE
) +
# ================= ADDITIVE =================
ggplot2::geom_line(
data = dplyr::filter(ac_long, type == "Additive"),
ggplot2::aes(x = var_id, y = value, color = method, group = method),
alpha = 0.85
) +
ggplot2::geom_point(
data = dplyr::filter(ac_long, type == "Additive"),
ggplot2::aes(x = var_id, y = value, color = method, shape = method),
size = 2
) +
ggplot2::scale_color_manual(
name = "Additive",
values = my_colors,
breaks = add_present,
drop = FALSE,
guide = ggplot2::guide_legend(order = 1, override.aes = list(shape = my_shapes[add_present]))
) +
ggplot2::scale_shape_manual(
name = "Additive",
values = my_shapes,
breaks = add_present,
drop = FALSE
) +
ggplot2::guides(shape = "none") +
ggnewscale::new_scale_color() +
ggnewscale::new_scale("shape") +
# ================= NON-ADDITIVE =================
ggplot2::geom_line(
data = dplyr::filter(ac_long, type == "Non-additive"),
ggplot2::aes(x = var_id, y = value, color = method, group = method),
alpha = 0.85
) +
ggplot2::geom_point(
data = dplyr::filter(ac_long, type == "Non-additive"),
ggplot2::aes(x = var_id, y = value, color = method, shape = method),
size = 2
) +
ggplot2::scale_color_manual(
name = "Non-additive",
values = my_colors,
breaks = nonadd_present,
drop = FALSE,
guide = ggplot2::guide_legend(order = 2, override.aes = list(shape = my_shapes[nonadd_present]))
) +
ggplot2::scale_shape_manual(
name = "Non-additive",
values = my_shapes,
breaks = nonadd_present,
drop = FALSE
) +
ggplot2::guides(shape = "none") +
ggplot2::ylab("alienation coefficient") +
ggplot2::theme_bw() +
ggplot2::scale_x_continuous(
breaks = seq(1, 14, 1),
labels = meas_to_plot_ac$variable
) +
ggplot2::theme(
axis.text.x = ggplot2::element_text(angle = 60, hjust = 1),
legend.position = "bottom",
legend.title.position = "top",
legend.text = element_text(size = 13)
) +
ggplot2::xlab("") +
ggplot2::facet_wrap(. ~ additive)
ac_plot
```
```{r,echo=FALSE,eval=FALSE}
ggsave("figure_5_ac_rel_importances.pdf", ac_plot, width = 8, height = 4)
```
<!-- ## Clustering based comparison -->
<!-- ### Real dataset setup -->
<!-- ```{r real-dataset-setup} -->
<!-- #| code-fold: false -->
<!-- real_data_flow <- tibble( -->
<!-- dataset_path = paste0("data/",c("cleveland5.Rdata","cleveland2.Rdata","dermatology.Rdata", -->
<!-- "obesitas.Rdata", "australian.Rdata")) -->
<!-- ) |> mutate( -->
<!-- dataset_name =c("cleveland5","cleveland2","dermatology", -->
<!-- "obesitas", "australian"), -->
<!-- loaded_data= purrr::map(.x = dataset_path, .f=function(x=.x){ -->
<!-- temp_env = new.env() -->
<!-- load(x, envir = temp_env) -->
<!-- return(as.list(temp_env)) -->
<!-- } -->
<!-- ), -->
<!-- dataset= purrr::map(.x = loaded_data, .f= ~as_tibble(.x$df) |> select(-.x$t)), -->
<!-- label = purrr::map(.x = loaded_data, .f = ~{ -->
<!-- df <- as_tibble(.x$df) -->
<!-- target <- .x$t -->
<!-- pull(df, target) -->
<!-- }), -->
<!-- n_clusters= purrr::map_int(.x = loaded_data, .f = ~.x$k) -->
<!-- ) -->
<!-- method = c("baseline","naive","hl","hl_add","gower","gudmm","dkss","mod_gower","u_ind","u_dep") -->
<!-- # Dataset-specific continuous feature counts for GUDMM, KDML, and EDMIX -->
<!-- dataset_cont_features <- tibble( -->
<!-- dataset_name = c("cleveland5", "cleveland2", "dermatology", "obesitas", "australian"), -->
<!-- no_f_cont = c(5, 5, 1, 8, 8) -->
<!-- ) -->
<!-- # Create the scenario structure first -->
<!-- clu_scenario_structure = crossing(real_data_flow |> -->
<!-- select(-dataset_path), method) |> -->
<!-- filter(!(dataset_name == "obesitas" & method == "dkss")) -->
<!-- ``` -->
<!-- ```{r clustering_experiments} -->
<!-- # set.seed(123) -->
<!-- set.seed(12) -->
<!-- pb_clu <- progress_bar$new( -->
<!-- format = "clustering [:bar] :percent eta: :eta", -->
<!-- total = nrow(real_data_flow) * length(methods), -->
<!-- clear = FALSE, -->
<!-- width = 60 -->
<!-- ) -->
<!-- #| code-fold: false -->
<!-- cluster_results = clu_scenario_structure |> -->
<!-- mutate( -->
<!-- distance_matrix = map2(.x=dataset, .y=method, -->
<!-- ~distance_by_method(df=.x, method = .y) -->
<!-- ) -->
<!-- ) |> -->
<!-- mutate( -->
<!-- clustering = map2(.x=distance_matrix, .y=n_clusters, -->
<!-- function(x=.x,y=.y){pb_clu$tick() -->
<!-- if (y > 1) { -->
<!-- return(cluster::pam(x, k = y,nstart = 10)$clustering) -->
<!-- } else { -->
<!-- return(NULL) # No clustering for single cluster -->
<!-- } -->
<!-- } -->
<!-- ), -->
<!-- ari = map2_dbl(clustering, label, ~{ -->
<!-- if (is.null(.x)) { -->
<!-- return(NA) -->
<!-- } else { -->
<!-- return(round(ARI(.x, .y), digits = 3)) -->
<!-- } -->
<!-- }) -->
<!-- ) -->
<!-- save(file="cluster_results.RData", cluster_results) -->
<!-- ``` -->
<!-- ```{r clustering_experiments} -->
<!-- cluster_aris = cluster_results |> -->
<!-- select(dataset_name, method, ari)|> pivot_wider(names_from=method, values_from=ari) |> -->
<!-- mutate(across(where(is.numeric), ~round(.x, digits = 3))) -->
<!-- cluster_aris_long= cluster_aris |> mutate(data_x_ax=1:nrow(cluster_aris)) |> -->
<!-- pivot_longer(cols = -c(dataset_name,data_x_ax), names_to = "method", values_to = "ari") |> -->
<!-- mutate(method = factor(method, levels = c("naive","hl","hl_add","gower","gudmm","dkss","mod_gower","u_ind","u_dep"))) -->
<!-- my_colors <- c( -->
<!-- # "baseline" = "#666666", # -->
<!-- "naive" = "#d95f02", # orange -->
<!-- "hl" = "#7570b3", # purple -->
<!-- "hl_add" = "#1b9e77", # green -->
<!-- "gower" = "#e7298a", # pink -->
<!-- "gudmm" = "#66a61e", # olive green -->
<!-- "dkss" = "#e6ab02", # mustard -->
<!-- "mod_gower" = "#a6761d", # brown -->
<!-- "u_ind" = "dodgerblue", -->
<!-- "u_dep" = "indianred" -->
<!-- ) -->
<!-- cluster_plot = cluster_aris_long |> ggplot(aes(x=data_x_ax,y=ari, color=method)) + -->
<!-- geom_point()+geom_line(aes(lty=method)) + -->
<!-- scale_color_manual(values = my_colors) + -->
<!-- theme(legend.position = "right")+ -->
<!-- theme_minimal() + -->
<!-- scale_x_continuous(breaks=seq(1,nrow(cluster_aris),1),labels =cluster_aris$dataset_name)+labs(x="",y="adjusted rand index") -->
<!-- ggsave(cluster_plot, file = "cluster_plot.pdf", width = 8, height = 4) -->
<!-- ``` -->
<!-- ```{r} -->
<!-- # method_performance <- cluster_aris %>% -->
<!-- # group_by(method) %>% -->
<!-- # summarise( -->
<!-- # mean_ari = mean(ari, na.rm = TRUE), -->
<!-- # sd_ari = sd(ari, na.rm = TRUE), -->
<!-- # median_ari = median(ari, na.rm = TRUE), -->
<!-- # min_ari = min(ari, na.rm = TRUE), -->
<!-- # max_ari = max(ari, na.rm = TRUE), -->
<!-- # n_datasets = sum(!is.na(ari)), -->
<!-- # .groups = 'drop' -->
<!-- # ) %>% -->
<!-- # arrange(desc(mean_ari)) -->
<!-- performance_plot <- cluster_aris |> -->
<!-- filter(!is.na(ari)) |> -->
<!-- ggplot(aes(x = method, y = ari, fill = method)) + -->
<!-- geom_boxplot() + -->
<!-- coord_flip() + -->
<!-- labs( -->
<!-- title = "Clustering Performance Comparison", -->
<!-- subtitle = "ARI scores across all datasets", -->
<!-- x = "Method", -->
<!-- y = "Adjusted Rand Index (ARI)", -->
<!-- fill = "Method Type" -->
<!-- ) + -->
<!-- theme_minimal() + -->
<!-- theme(legend.position = "bottom") -->
<!-- # print("Method Performance Summary:") -->
<!-- # print(method_performance) -->
<!-- # Dataset-specific results -->
<!-- dataset_results <- cluster_results %>% -->
<!-- group_by(dataset_name) %>% -->
<!-- summarise( -->
<!-- best_method = method[which.max(ari)], -->
<!-- best_ari = max(ari, na.rm = TRUE), -->
<!-- worst_ari = min(ari, na.rm = TRUE), -->
<!-- ari_range = best_ari - worst_ari, -->
<!-- .groups = 'drop' -->
<!-- ) -->
<!-- ``` -->
## Appendix D Categorical mean distances: skewed distributions
```{r}
LeHo<-function(X){ # Returns the LeHo Distance (symmetric Kullback-Leibler)
# X is matrix with conditional probabilities
#if(any(rowSums(X)!=1)){
# print("Input must be conditional probs (row sums should be 1)")
#} else {
require(philentropy)
n<-nrow(X)
D<-matrix(0,n,n)
for (i in 1:(n-1)){
for (j in (i+1):n){
D[j,i]<-D[i,j]<-distance(X[c(i,j),],"kullback-leibler",unit="log2")+
distance(X[c(j,i),],"kullback-leibler",unit="log2")}
}
return(D)
}
```
### Data generation
```{r,messge=FALSE, warning=FALSE}
# Let's consider some specific unbalanced scenarios
# One probility is d. The others are (1-d)/(q-1)
# We consider skewed options:
dis<-c(0.05,0.1,0.2,0.33,0.5,0.66,0.8,0.9,0.95)
#qi=5
qs<-c(2,3,5,10)#,18) # Some options for qi
nint<-length(dis) # Number of options for d (nint-1)
rsm<-rsma<-rhl<-sdsm<-rse<-rsof<-rsiof<-sdse<-rsa<-sdsa<-sdsof<-sdsiof<-sddsma<-sdssm<-
sddse<-sddsa<-sddsm<-sdhl<-sddsmca<-sddsof<-sddsiof<-sddshl<- sdshl<-
rsmca<-sdsmca<-esm<-em<-ee<-ea<-ehl<-emca<-eof<-eiof<-matrix(NA,nrow=nint,ncol=length(qs))
#par(mfrow=c(2,2))
for (qis in 1:length(qs)){
#ds<-NULL
qi<-qs[qis]
for (i in (1:nint)){ # variant 2
Deltam<-matrix(1,qi,qi) # Matching
diag(Deltam)<-rep(0,qi) # Matching Delta
#d=i/(2*qi) # i=2 corresponds to equal probs if variant 1 is chosen. (Only works for one qi. Not for qs loop)
d=dis[i] # variant 2
#ds<-rbind(ds,d)
p<-c(d,rep((1-d)/(qi-1),(qi-1)))
sum(p)
Dp<-diag(p)
pp<-p %*% t(p)
spi<-(diag(Dp-pp))^-1
spi5<-(diag(Dp-pp))^-.5
DEsk<-(2/(qi^2))*Deltam # Delta Eskin
DOF<-log(p)%*%t(log(p)) * Deltam # OF
n=160 # For inv OF we need n. Soon gets very large (increases in n) 160 is sufficient
#n<-ceiling(1/min(p))
DIOF<-log(n*p)%*%t(log(n*p)) * Deltam # inverse OF. If some np<1 we can get negatives
n=160 # For HL we need to find a way to get somewhat consistent values. Let's choose n large
marginals=p*n
HLemp<-distancefactor(cat=qi,n=n,catsizes=marginals) #
DHL<-Deltam*HLemp*2#*sqrt(2) # NOTE 13/09: Corrected: Was sqrt(2). But, should be, see paper, 2x
#DE<-sqrt((1/qi)*(spi %*% t(rep(1,qi)) + t(spi %*% t(rep(1,qi)))))
#diag(DE)<-rep(0,qi)
DM<-sqrt(1/qi)*(spi5 %*% t(rep(1,qi)) + t(spi5 %*% t(rep(1,qi))))
diag(DM)<-rep(0,qi)
DA<-(1/qi)*diag(spi5)%*%Deltam%*%diag(spi5)
DMCA<-(1/qi) * diag(p^-.5)%*%Deltam%*%diag(p^-.5)
#we<-ee[i,(qis)]<- t(p)%*%DE%*%p
wsm<-esm[i,(qis)]<- t(p)%*%Deltam%*%p # Simple Matching
we<-ee[i,(qis)]<- t(p)%*%DEsk%*%p # Eskin
wof<-eof[i,(qis)]<-t(p)%*%DOF%*%p # OF
wiof<-eiof[i,(qis)]<-t(p)%*%DIOF%*%p # IOF
whl<-ehl[i,(qis)]<-t(p)%*%DHL%*%p # HL
wm<-em[i,(qis)]<- t(p)%*%DM%*%p # SD scaling
wa<-ea[i,(qis)]<- t(p)%*%DA%*%p # Cat dis scaling
wmca<-emca[i,(qis)]<- t(p)%*%DMCA%*%p # MCA scaling
# We can also estimate the variance among the distances using Deltas: E(X^2)-E(X)^2
# We can do this dividing by expected values so that we look at what happens
# when delta is commensurable. Or not
# if not:
#we<-wm<-wa<-wmca<-wof<-wiof<-whl<-wsm<-1
sddse[i,(qis)]<- sqrt(t(p)%*%DEsk^2%*%p - ee[i,(qis)]^2)/we # Eskin
sddsma[i,(qis)]<- sqrt(t(p)%*%Deltam^2%*%p - esm[i,(qis)]^2)/ wsm # Simple Matching
sddshl[i,(qis)]<- sqrt(t(p)%*%DHL^2%*%p - ehl[i,(qis)]^2)/ whl # HL
sddsm[i,(qis)]<- sqrt(t(p)%*%DM^2%*%p - em[i,(qis)]^2)/ wm # SD
sddsa[i,(qis)]<- sqrt(t(p)%*%DA^2%*%p - ea[i,(qis)]^2)/wa # Cat dissim
sddsmca[i,(qis)]<- sqrt(t(p)%*%DMCA^2%*%p - emca[i,(qis)]^2)/wmca # MCA
sddsof[i,(qis)]<-sqrt(t(p)%*%DOF^2%*%p - eof[i,(qis)]^2)/wof # OF
sddsiof[i,(qis)]<-sqrt(t(p)%*%(DIOF/as.numeric(wiof))^2%*%p - 1 ) #IOF
# Let's consider spread among cat dissimilarities. But: This only makes sense
# when on similar scales. So, use commensurable deltas: (Or not: see above)
sdse[i,qis]<-sd((1/we)*DEsk[upper.tri(DEsk)]) # Eskin
sdsm[i,qis]<-sd((1/wm)*DM[upper.tri(DM)]) # SD
sdshl[i,qis]<-sd((1/whl)*DHL[upper.tri(DHL)]) # HL
sdssm[i,qis]<-sd((1/wsm)*Deltam[upper.tri(Deltam)]) # Simple Matching
sdsa[i,qis]<-sd((1/wa)*DA[upper.tri(DA)]) # Cat dissim,
sdsmca[i,qis]<-sd((1/wmca)*DMCA[upper.tri(DMCA)]) # MCA
sdsof[i,qis]<-sd((1/wof)*DOF[upper.tri(DOF)]) # OF
sdsiof[i,qis]<-sd((1/wiof)*DIOF[upper.tri(DIOF)]) # IOF
}
}
cats<-as.character(qs)
skew<-as.character(dis)#as.character(1:nint)
```
### Code for `Figure 7`
```{r,fig.height=7,fig.width=7}
sk_distance_to_plot = function(exp_mean_dist,distance_name){
exp_mean_dist = as_tibble(exp_mean_dist) |> mutate(`skewness (p1)` = c(0.05,0.1,0.2,0.33,0.5,0.66,0.8,0.9,0.95)) |>
rename(`2 cats` = V1,
`3 cats` = V2,
`5 cats` = V3,
`10 cats` = V4) |>
mutate(method=distance_name) |>
pivot_longer(cols = c(`2 cats`, `3 cats`, `5 cats`, `10 cats`),
names_to = "Number of categories", values_to = "Mean distance")
return(exp_mean_dist)
}
all_exp_mean_dist=rbind(sk_distance_to_plot(esm,"Simple Matching"),
sk_distance_to_plot(ee,"Eskin"),
sk_distance_to_plot(eof,"OF"),
sk_distance_to_plot(eiof,"IOF")
)
paper_plot_skew1=all_exp_mean_dist |>
mutate(`Number of categories`=fct_inorder(`Number of categories`),
method=fct_inorder(method),) |>
ggplot(aes(y=`Mean distance`,x=`skewness (p1)`,color=`Number of categories`)) +
geom_line() + geom_point() + facet_wrap(~method,scales = "free_y") + theme_minimal() + labs(x=expression("Skewness (p1)"), y="Mean distance") +
xlim(c(0,1))+expand_limits(y = 0)+theme_bw()+theme(legend.position = "bottom")
print(paper_plot_skew1,width=10,height=6)
```
### Code for `Figure 8`
```{r,fig.height=4,fig.width=8}
all_exp_mean_dist2=rbind(sk_distance_to_plot(ehl,"Hennig-Liao"),
sk_distance_to_plot(em,"Std. dev."),
sk_distance_to_plot(ea,"Cat. dissim.")
)
paper_plot_skew2=all_exp_mean_dist2 |>
mutate(`Number of categories`=fct_inorder(`Number of categories`),
method=fct_inorder(method),) |>
ggplot(aes(y=`Mean distance`,x=`skewness (p1)`,color=`Number of categories`)) +
geom_line() + geom_point() + facet_wrap(~method) + theme_minimal() + labs(x=expression("Skewness (p1)"), y="Mean distance") +
xlim(c(0,1))+expand_limits(y = 0)+theme_bw()+theme(legend.position = "bottom")
print(paper_plot_skew2)
```
### Code for `Figure 9`
```{r,fig.height=4,fig.width=8}
qs<-c(2,3,5,10)#,18) # Some options for qs
nint<-length(dis) # Number of options for d (nint-1)
CVchd<-CVtvd<-CVmsd<-CVlhd<-Echi<-Echd<-Etvi<-Etvd<-Emsi<-Elhi<-Elhd<-Emsd<-array(NA,dim=c(length(qs),length(qs),nint,nint))
for (q1 in 1:length(qs)){ # cats row
qi<-qs[q1]
for (q2 in q1:length(qs)){ # cats cols
qj<-qs[q2]
for (pi in 1:nint){ # row distributions
d1<-dis[pi]
p1<-c(d1,rep((1-d1)/(qj-1),(qj-1))) # nint different marginals: Distribution over colums
for (pj in 1:nint){
d2<-dis[pj]
p2<-c(d2,rep((1-d2)/(qi-1),(qi-1))) # corresponding col marginals: Distribution over rows
Pi<-p2 %*% t(p1) # joint table independent
Ri<-Pi/rowSums(Pi) # conditional table independent
# Ci<-Ri/sqrt(p2)
if (qj>qi) {
Pd<-diag(p1[1:qi])
Addzeros<-matrix(0,(qi-1),(qj-qi))
Addps<-p1[qi+1:(qj-qi)]
Add<-rbind(Addzeros,Addps)
Pd<-cbind(Pd,Add)
} else { #qi=qj
pd<-p2
Pd<-diag(pd) # joint table dependent case (diagonal smallest q)
}
Rd<-Pd/rowSums(Pd)
Cd<-Rd/sqrt(p2) # Chi-square table: cond. prob/sqrt(p)
# category dissimilarities:
Dlhd<-LeHo(Rd) # Le Ho
# Dmsd<-MousaviSehhati(Pd) # Moussavi
Dtvd<-dist(Rd,"manhattan")/2 # TVD
Dchd<-dist(Cd,"euclidean")^2 # Chi2 dist
# Dchd<-Dchd/(2*(qi-1)) # Chi2 dist corrected for number of categories...
Elhd[q1,q2,pi,pj]<-t(pd) %*%Dlhd %*%pd
# Emsd[q1,q2,pi,pj]<-t(pd) %*%Dmsd %*%pd
Etvd[q1,q2,pi,pj]<-t(pd) %*%as.matrix(Dtvd) %*%pd
Echd[q1,q2,pi,pj]<-t(pd) %*%as.matrix(Dchd) %*%pd
# Coefficient of variation
CVlhd[q1,q2,pi,pj]<-sqrt(t(pd) %*%Dlhd^2 %*%pd - (t(pd) %*%Dlhd %*%pd)^2)/(t(pd) %*%Dlhd %*%pd)
# CVmsd[q1,q2,pi,pj]<-sqrt(t(pd) %*%Dmsd^2 %*%pd - (t(pd) %*%Dmsd %*%pd)^2)/(t(pd) %*%Dmsd %*%pd)
CVtvd[q1,q2,pi,pj]<-sqrt(t(pd) %*%(as.matrix(Dtvd))^2 %*%pd - (t(pd) %*%as.matrix(Dtvd) %*%pd)^2)/(t(pd) %*%as.matrix(Dtvd) %*%pd)
CVchd[q1,q2,pi,pj]<-sqrt(t(pd) %*%(as.matrix(Dchd))^2 %*%pd - (t(pd) %*%as.matrix(Dchd) %*%pd)^2)/(t(pd) %*%as.matrix(Dchd) %*%pd)
Dlhi<-LeHo(Ri)
# Dmsi<-MousaviSehhati(Pi)
Dtvi<-dist(Ri,"manhattan")/2
# Dchi<-dist(Ci,"euclidean")^2
Elhi[q1,q2,pi,pj]<-t(p2) %*%Dlhi %*%p2
# Emsi[q1,q2,pi,pj]<-t(p2) %*%Dmsi %*%p2
Etvi[q1,q2,pi,pj]<-t(p2) %*%as.matrix(Dtvi) %*%p2
# Echi[q1,q2,pi,pj]<-t(p1) %*%as.matrix(Dchi) %*%p1
}
}
}
}
Elhs<-as.data.frame(rbind(Elhd[1,1,1,],Elhd[2,2,1,],Elhd[3,3,1,],Elhd[4,4,1,]))
Etvs<-as.data.frame(rbind(Etvd[1,1,1,],Etvd[2,2,1,],Etvd[3,3,1,],Etvd[4,4,1,]))
Emss<-as.data.frame(rbind(Emsd[1,1,1,],Emsd[2,2,1,],Emsd[3,3,1,],Emsd[4,4,1,]))
Echs<-as.data.frame(rbind(Echd[1,1,1,],Echd[2,2,1,],Echd[3,3,1,],Echd[4,4,1,]))
CVlhs<-as.data.frame(rbind(CVlhd[1,1,1,],CVlhd[2,2,1,],CVlhd[3,3,1,],CVlhd[4,4,1,]))
CVtvs<-as.data.frame(rbind(CVtvd[1,1,1,],CVtvd[2,2,1,],CVtvd[3,3,1,],CVtvd[4,4,1,]))
CVmss<-as.data.frame(rbind(CVmsd[1,1,1,],CVmsd[2,2,1,],CVmsd[3,3,1,],CVmsd[4,4,1,]))
CVchs<-as.data.frame(rbind(CVchd[1,1,1,],CVchd[2,2,1,],CVchd[3,3,1,],CVchd[4,4,1,]))
cats<-as.character(qs)
skew<-as.character(dis)#as.character(1:nint)
sk_distance_to_plot = function(exp_mean_dist,distance_name){
exp_mean_dist = as_tibble(exp_mean_dist) |> mutate(`skewness (p1)` = c(0.05,0.1,0.2,0.33,0.5,0.66,0.8,0.9,0.95)) |>
rename(`2 cats` = V1,
`3 cats` = V2,
`5 cats` = V3,
`10 cats` = V4) |>
mutate(method=distance_name) |>
pivot_longer(cols = c(`2 cats`, `3 cats`, `5 cats`, `10 cats`),
names_to = "Number of categories", values_to = "Mean distance")
return(exp_mean_dist)
}
all_exp_mean_dist3=rbind(sk_distance_to_plot(t(as.matrix(Elhs)),"Le-Ho"),
sk_distance_to_plot(t(as.matrix(Etvs)),"Total Variance Distance")
)
paper_plot_skew3=all_exp_mean_dist3 |>
mutate(`Number of categories`=fct_inorder(`Number of categories`),
method=fct_inorder(method),) |>
ggplot(aes(y=`Mean distance`,x=`skewness (p1)`,color=`Number of categories`)) +
geom_line() + geom_point() + facet_wrap(~method,scales="free_y") + theme_minimal() + labs(x=expression("Skewness (p1)"), y="Mean distance") +
xlim(c(0,1))+expand_limits(y = 0)+theme_bw()+theme(legend.position = "bottom")
print(paper_plot_skew3,width=8,height=4)
```
## Appendix E FIFA variable distributions
### Code for `Figure 10`
```{r, fig.height=12,fig.width=8}
# load("data/Fifa21NL.RData") # Load the data
data(fifa_nl,package="manydist")
#Xorig<-X<-ddata[,-c(1,2)]
Xorig<-X<-fifa_nl[,-c(1,2,19:24)] # vars 1 and 2 are a bit useless (too many categories)
# vars 19:24 interesting but same scale and little variation
# leaving them out makes the plots a bit smaller.
# leaving them in doesn't seem to change a lot
n<-nrow(X)
# p<-ncol(X)
K<-10 # Number of clusters in cluster analysis
nd<-2 # Dimensionality of MDS solution
X=X[,c(8:1,9:16)] # Order
Xorig=Xorig[,c(8:1,9:16)] # Order
X=X[,-3] # Remove int rep: 380 have something, 21+7 in other cats
Xorig=Xorig[,-3]
X=X[,c(1:12,14,13,15)]
Xorig=Xorig[,c(1:12,14,13,15)]
p<-ncol(X)
# First convert integers to numeric manually
X[8:15] <- lapply(X[8:15], as.numeric)
# reordering / numeric first
X <- X %>%
select(where(is.integer), where(is.numeric), where(is.factor))
X_tib_num = X |> as_tibble() |> select(where(is.numeric))
X_tib_cat = X |> as_tibble() |> select(where(is.factor))
levels(X_tib_cat$work_rate)=c("H/H", "H/L", "H/M", "L/H", "L/L", "L/M", "M/H", "M/L", "M/M")
levels(X_tib_cat$club_name) = c("ADO","Ajax","AZ","Emmen","Groningen","Twente","Utrecht",
"Feyenoord","Fortuna","Heracles","PEC","PSV","RKC","Heerenveen",
"Sparta","Vitesse","VVV","Willem II")
X_tib_cat=X_tib_cat |> rename(`club`=club_name,
`position`=team_position)
X_tib_num_nest = tibble(values=X_tib_num |> map((~.x)),features=names(X_tib_num))|>
mutate(
hplot=map2(.x=values,.y=features,
function(x=.x,y=.y){
my_tib=tibble(a=x)
names(my_tib) = y
my_plot= my_tib |> ggplot(aes(x)) + geom_histogram(bins=15,alpha=.75)+theme_bw()+ggtitle(y)+
theme(plot.title = element_text(hjust = 0.5))+xlab("")+ylab("")
}
)
)
X_tib_cat_nest = tibble(values=X_tib_cat |> map((~.x)),features=names(X_tib_cat))|>
mutate(
bplot=map2(.x=values,.y=features,
function(x=.x,y=.y){
my_tib=tibble(a=x)
names(my_tib) = y
my_plot= my_tib |> ggplot(aes(x)) + geom_bar(alpha=.75)+theme_bw()+ggtitle(y)+
theme(plot.title = element_text(hjust = 0.5),
axis.text.x =element_text(angle=90 ))+xlab("")+ylab("")
}
)
)
fifa_descriptive_plots=(X_tib_cat_nest$bplot[[1]]/
X_tib_cat_nest$bplot[[2]]/
X_tib_cat_nest$bplot[[3]]/
X_tib_cat_nest$bplot[[4]]/
X_tib_cat_nest$bplot[[5]]/
X_tib_cat_nest$bplot[[6]]/
X_tib_cat_nest$bplot[[7]])|
(X_tib_num_nest$hplot[[1]]/
X_tib_num_nest$hplot[[2]]/
X_tib_num_nest$hplot[[3]]/
X_tib_num_nest$hplot[[4]]/
X_tib_num_nest$hplot[[5]]/
X_tib_num_nest$hplot[[6]]/
X_tib_num_nest$hplot[[7]])#+ plot_layout(guides = 'collect')
print(fifa_descriptive_plots)
```
